Efficient mixed representation of active and passive motion in the mouse visual thalamus during natural behaviour

Efficient mixed representation of active and passive motion in the mouse visual thalamus during natural behaviour | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Efficient mixed representation of active and passive motion in the mouse visual thalamus during natural behaviour A.S. Ebrahimi , M.P. Hogan , F. Jin , F.P. Martial , Q. Huang , R. Joshi , K. Shirvanian , M. Burgess , Z. Montazeri , R.S. Petersen , R. Storchi doi: https://doi.org/10.1101/2025.11.03.686375 A.S. Ebrahimi 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site M.P. Hogan 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site F. Jin 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site F.P. Martial 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site Q. Huang 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site R. Joshi 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site K. Shirvanian 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site M. Burgess 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site Z. Montazeri 2 University of Manchester, School of Engineering, Department of Computer Science Find this author on Google Scholar Find this author on PubMed Search for this author on this site R.S. Petersen 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site R. Storchi 1 University of Manchester, School of Biological Sciences, Division of Neuroscience Find this author on Google Scholar Find this author on PubMed Search for this author on this site For correspondence: riccardo.storchi{at}manchester.ac.uk Abstract Full Text Info/History Metrics Supplementary material Data/Code Preview PDF Abstract During natural behaviour, changes in the visual scene are largely driven by the subject’s own movements, which can be actively generated (e.g., walking) or passively imposed by external forces (e.g., riding a vehicle). How the visual system represents such active and passive motion components is poorly understood. To address these questions, we developed an assay to dissect the motion of freely moving mice into active and passive components and to study its influence upon neural activity in the dorsal lateral geniculate nucleus (dLGN) and adjacent regions. Chronically implanted mice were placed in an arena where they actively moved; at irregular intervals, the arena was tilted, resulting in passive movement. We then used 3D tracking to decompose mouse head motion into active and passive components. We observed widespread responses to tilt events in dLGN, which persisted in darkness. Light-responsive units exhibited mixed selectivity for active and passive motion, primarily encoding the speed of self-motion irrespectively of its causes. However, individual neurons varied in their relative tuning to active versus passive components, allowing partial separation at the population level. Furthermore, a decoding analysis showed that population activity decorrelated active and passive head motion signals by representing their leading principal components. Together, these results indicate that, during natural behaviour, the visual thalamus takes advantage of the coupled dynamics of active and passive movements to encode an efficient, low-dimensional representation of the subject’s motion. Introduction In daily life, both voluntary and externally imposed movements continuously shape the patterns of light hitting the retina and how we perceive the visual world. Thus, animals express active motion (e.g. locomotion, eye and head movements) to explore and interact with the environment but are also subject to unexpected or passive motion (e.g. slipping on unstable terrain, being pushed by external forces). Previous studies on head-fixed animals have shown that both are represented along the visual pathways [ 1 - 8 ]. However, in freely moving animals these two forms of motion can be coupled and often happen at the same time, since active movements are frequently recruited to counteract the destabilising effects of passive displacements (e.g. humans step forward or backward to maintain balance, [ 9 ]). How active and passive motion are jointly represented in the visual system during natural behaviour is currently unknown. On the one hand, active and passive motions could be encoded by separate pools of cells. Such separation would enable the visual system to differentially process visual information according to its underlying causes (e.g. walking vs being pushed). Neural circuits isolating passive motion signals that deviate from proprioceptive expectations driven by motor commands have been recently described at the level of the cerebellar cortex [ 10 ]. The outputs of such circuits is conveyed to deep cerebellar nuclei and brainstem regions [ 11 , 12 ] and can reach thalamocortical circuits [ 13 - 15 ]. On the other hand, the visual system might favour efficiency. A key principle of efficient coding is to minimise redundant information [ 16 ] and this can be achieved by employing cells with mixed selectivity [ 17 - 20 ]. Thus, a mixed representation of active and passive motion that takes advantage of the correlations between these motion components would be preferable. In support of this possibility, a recent study has indeed shown that the same cells in primary visual cortex integrate active and passive head motion [ 3 ]. Discriminating between these diverse encoding strategies requires the ability to capture the ethologically relevant statistics of active and passive motion during natural behaviour. Yet, the effect of active and passive motion on visual signalling has been traditionally studied in head-fixed animals. These studies provided fundamental information to help us to understand how the tuning of visual responses is affected by active and passive motion and the neural circuits mediating such effects [ 1 , 2 , 4 , 21 ]. However, such experiments cannot fully capture the coupled temporal dynamics of active and passive motion expressed during natural behaviour (e.g. when active motion is required to adjust posture and maintain balance) and the natural synergies between eye, head and body movements. To address this gap, we took advantage of recent advances in tracking technology and 3D video reconstruction [ 6 , 22 , 23 ]. We developed a behavioural assay where freely moving animals were placed on a motorised arena that induced passive motion of the animal in the form of controlled tilts. By 3D reconstruction, we were then able to disambiguate animal’s passive motion, induced by the tilting of the arena, from active motion, generated by the animal’s voluntary movements, even when these motion components occurred simultaneously. We implanted these animals with Neuropixel 1.0 probes [ 24 ] primarily targeting the dorsal lateral geniculate nucleus (dLGN), the primary thalamic relay of retinal input to the cortex, known to also respond to locomotion and head posture [ 6 - 8 ]. These electrodes also enabled us to simultaneously record from visually responsive neurons in neighbouring thalamic and subthalamic regions, capturing a broad view of subcortical visual processing. Firstly, we found that tilt events evoked transient increases in firing rate in many light responsive cells. These responses were also observed in the dark, confirming their nonvisual nature, and were not simply a reflection of “surprise” since could be also observed when tilt occurrence was made predictable by delivering a sound cue. We then set out to determine how the neural responses depended on active vs passive head motion. A clustering analysis revealed four main classes of responses uniformly distributed in thalamic but not subthalamic regions. All classes encoded mixed representations of active and passive head speed but assigned different weights to them. A population decoding analysis showed that such mixed representations encoded the leading principal component of motion signals, corresponding to the combined active and passive head speed (first component) and the difference between these signals (second component). These results indicate that the visual thalamus encodes a low-dimensional, mixed representation of active and passive motion which is consistent with principles of efficient coding. Results A freely moving assay enables active and passive motion to be separated in freely moving animals We first aimed to establish a freely moving assay to separately quantify active and passive motion and their effect on neural activity. Naïve mice were placed in a small open field arena (20 x 20cm, Figure 1A ). Mice were videoed by 8 synchronised cameras ( Figure 1A ) and keypoints on both mouse and arena were tracked and 3D reconstructed by using custom developed software ( Figure 1B ; Supplementary Movie 1 ; see Methods ). Arena floor and walls were transparent but covered with a see-through metal grid that enabled animals to maintain a firm grip during postural perturbations generated by a servo motor. The perturbations consisted of left and right tilts delivered from the same initial position in which the arena floor was parallel to the ground. After each perturbation the arena was maintained in tilted position for 1s, then tilted back to its initial position ( Figure 1C ). Tilts induced head/body rolls when the mouse was oriented parallel to the tilt axis, or head/body pitch, when oriented perpendicular to the tilt axis. Since animals thoroughly explored the arena in each experimental session, we were able to collect a large sample of roll and pitch events induced by the tilt ( Figure 1D ). Download figure Open in new tab Figure 1. A) Schematic drawing of the behavioural recording set-up. B) Sample images from two cameras capturing the animal from different views, and the corresponding 3D reconstruction based on the full set of eight camera views. C) Rotation angles for left and right tilts and no tilt condition measured from 3D reconstructions of the behavioural videos. D) Histogram of the number of trials (Mean ± SEM; averaged across dataset of 9 animals) in which the animal head was oriented in specific directions (as shown on the x axis). E) Histological verification of the electrode placement. To visualise its position in the brain, the electrode was painted with fluorescent DIL marker before penetrating the brain. F) Raster plot of two visually responsive units. Arena illumination provided by monitors mounted on the arena sides is turned from DARK to BRIGHT at time 0. In a subset of trials (in which spikes are marked by black dots) the arena is maintained stationary. In the remaining trials (in which spikes are marked by blue dots) arena tilts are initiated at time 0. The light responses of these two units were not affected by the tilt. G) Same as panel F but here we show two units whose light responses were affected by the tilt. H) Same as panel F but here the arena is kept DARK throughout the trial. These two units show clear responses to the tilt. I) An example trial showing normalised readouts of tilt angle, angular passive head speed ( a PM ), linear passive head speed ( l PM ), angular active head speed ( a AM ) and linear active head speed ( l AM ). On the right, we show two mouse poses recorded at two different time points (indicated by asterisks) within the trial. The 3D coordinates reconstructed from the video are indicated by dots (Tracked 3D Coordinates). We compute the tilt angle of the arena, and we subtract it from the 3D coordinates to obtain “Tilt Removed” 3D coordinates (indicated by empty circles). We use this strategy as building block to disambiguate active and passive motion (see Methods ). J) Angular head speed for active (blue) and passive (red) motion. K) Linear head speed for active (blue) and passive (red) motion. L) Example image of the mouse eye obtained during our experiments. Labelling of the eye landmarks are shown in green. M) Eye speed (normalised by z-score) during platform tilts (blue) and when the platform was kept stationary (grey). N) Normalised cross-correlation of eye speed and active (blue) and passive (red) linear head speed. M) Normalised cross-correlation of eye speed and active (blue) and passive (red) linear head speed. Animals were implanted with Neuropixel 1.0 electrodes targeting primarily dLGN but also spanning more ventral thalamic and subthalamic nuclei ( Figure 1E , Supplementary Figure 1A, B ). To record neural responses to visual stimulation, four types of visual stimuli were delivered from monitors mounted around the arena: a step from dark to bright light (DARK-BRIGHT), a step from bright light to dark (BRIGHT-DARK), constant darkness (DARK-DARK) and constant bright light (BRIGHT-BRIGHT). The visual stimuli were combined with three tilt stimuli comprising a left tilt, a right tilt and no tilt. Combining visual and tilt stimulation we generated 12 distinct types of experimental trials (4 visual x 3 tilt, see protocol schematic in Supplementary Figure 1C ). The different visual stimuli were interleaved. The occurrence and direction of tilts followed a pseudorandom sequence to reduce the animal’s ability to predict them. For each animal, we recorded 400 trials (∼33 per condition). Statistical tests (see Methods ) were used to identify cells that were only responsive to visual stimulation ( Figure 1F ), cells whose visual responses were affected by tilts ( Figure 1G ) and cells that responded to tilts in the dark ( Figure 1H , Supplementary Figure 1B ). Download figure Open in new tab Supplementary Figure 1. A) Table showing the number of units we recorded across animals (rows) separated by their anatomical location (columns) as identified by our histological verification. B) Spike waveforms and raster plot for an example unit in our dataset. C) Schematic of the protocol for visual and tilt stimulation. Notice the 12 distinct trials encompassing all combinations of visual stimulation and tilts. D) Normalised pupil size during trials in which the platform was kept stationary (grey) or tilted (blue). E) Schematic of the modified protocol. Here a sound precedes the onset of the tilt and in these trials the platform is vibrated before the tilt onset. In trials in which the platform is kept stationary no sound or vibrations are delivered. F) Normalised pupil size during trials in which the platform was kept stationary (grey) or tilted (blue) for the modified protocol. Notice that here pupil size starts increasing the tilt onset at time 0. G-L) Same as Figure 2E, F, G, H, I, L , but here we report data collected during the modified protocol in panel E . Next, by focussing on animals’ head, we set-out to quantify passive motion, induced by the tilt, as well as active motion, expressed both as spontaneous movements and as motor reactions to the tilt. Three-dimensional reconstruction of keypoints on the animal and on the arena enabled us to separate these motion components. Thus, to isolate the active motion component, we first recalculated animal’s head coordinates during tilts by removing the tilt angle ( Figure 1I , Supplementary Movie 2 ). Conversely, to isolate the passive component, we calculated the transformation in the animal’s head coordinates induced by the tilt between pairs of consecutive frames while keeping the coordinates rigidly fixed to the arena reference frame. These calculations enabled us to estimate the linear and angular speed associated with active head motion ( l AM and a AM ) and passive head motion ( l PM , a PM ). A detailed description of these calculations is provided in Methods . Firstly, by measuring l AM and a AM , we found that both linear and angular speed for active motion peaked soon after the onset of the tilt, remained elevated while the arena was in tilted position, then quickly decreased after the arena tilted back to its initial position ( Figure 1J, K ). Secondly, by measuring l PM and a PM , we verified that both linear and angular speed for passive motion effectively captured the temporal dynamics of the tilts, showing two peaks in speed, which corresponded to the tilt away from, and back to, the initial arena position ( Figure 1J, K ). Since our measures of head motion did not directly take eye movements into account, we separately measured the relationship between head motion and eye motion. To this end, we implanted an additional set of animals (n=5) with miniaturised eye trackers ( Figure 1L, Supplementary Movie 3 ) and repeated the same behavioural protocols by jointly measuring l AM , a AM , l PM , a PM and the speed of eye movements. We found that, like for the head, the tilts induced fast increases in eye movements that followed the dynamics of the tilts ( Figure 1M ). A cross-correlation analysis revealed that eye movements were well synchronised with active and passive head motion ( Figure 1N, O ). Together, these results indicate that our measures of active and passive motion capture key aspects of both eye and head movements during postural perturbations. Cells in dLGN and neighbouring regions jointly encode light intensity and tilt events We first recorded neuronal responses to light stimulation without arena tilts to identify a dataset of light responsive cells (n=498). Within this dataset, visual stimulation evoked a variety of response types and a clustering algorithm, spanning a wide range of clustering solutions ( Methods ), identified 5 main classes ( Figure 2A, C , left panels; Figure 2B, D , orange lines ). We then measured visual responses from the same cells but during tilt events. We found that these events substantially affected firing rates ( Figure 2A, C , mid panels; Figure 2B, D , blue lines ). At single cell level, this effect was significant in a sizable fraction of cells, both in dLGN (41%, 119/290) and neighbouring regions (VPM: 30%, 20/67; ZI: 53%, 44/82; CP: 56%, 33/59). Moreover, the tilts affected all classes of light responses (p < 0.0001 for DARK-BRIGHT and p < 0.01 for BRIGHT-DARK across all 5 classes; sign-test, n = 150, 150, 87, 37, 74) and the net effect was a larger increase in firing rates compared with trials in which light stimulation was not paired with a tilt ( Figure 2E, F, G, H ). Individual classes differed in the amount to which firing rate was affected for responses to BRIGHT-DARK stimulation (p = 0.002, Χ 2 = 16.92, n = 498) but not for responses to DARK-BRIGHT stimulation (p = 0.12, Χ 2 = 7.33, n = 498). Download figure Open in new tab Figure 2. A) The left panel shows normalised PSTHs of single unit visual responses (DARK-BRIGHT) when the platform was kept stationary. Units are ordered along the y-axis according to a clustering analysis (see Methods ). The transition between clusters is shown by red lines. The middle panel shows the same units during the same light stimulation but recorded in trials in which arena tilts were initiated at time 0. The right panel shows the same units recorded in the dark during arena tilts. B) Average PSTH responses across the five classes of visual responses determined by our cluster analyses. Averages are separately calculated during DARK-BRIGHT visual stimulation when the platform was kept stationary (orange), during the same visual stimulation when the platform was tilted (blue) and during tilt stimulation in the dark (black). C) Same as panel A but here we recorded BRIGHT-DARK visual stimulation. The right panel is replicated from panel A for clarity of visualisation. D) Same as panel B but here we recorded BRIGHT-DARK visual stimulation. Black lines are replicated from panel A. E) Population responses (Mean ± SEM) to visual DARK-BRIGHT visual stimulation when the platform was kept stationary (x-axis) vs responses to the same visual stimulation during tilt events (y-axis). Cell populations are divided according to the class of visual response (same colour convention used in panel B. F) Changes in visual responses for each class (Mean ± SEM) obtained by subtracting visual responses during tilt stimulation from visual responses in absence of tilt. G) Same as panel E but here we recorded BRIGHT-DARK responses. H) Same as panel F but here we recorded BRIGHT-DARK responses. I) Goodness-of-fit, measured as R 2 for the three models described in the main text during DARK-BRIGHT visual stimulation. A linear combination of light and tilt responses explains single unit PSTHs better than a scaled response of the visual response alone and not significantly worse than a more complex model introducing a multiplicative interaction of visual and tilt response. L) Same as panel I but here we recorded BRIGHT-DARK visual stimulation. If the tilt effect was visually driven (e.g. by fast movements of the visual scene projected on the animal’s retina) we would expect it to disappear in the dark. To test for this possibility, we delivered an additional pseudorandomised sequence of tilts (n=100 trials) after turning off all monitors and all the other light sources in the room. We found that a comparable fraction of units (dLGN: 34%, 99/290; VPM: 30%, 20/67; ZI: 45%, 37/82; CP: 63%, 37/59) responded to tilts in the dark ( Figure 2A, C , right panels; Figure 2C, D , black lines ). Moreover, a sizable fraction of units whose light responses were modified by the tilt also responded to tilt in the dark (dLGN: 19%, 55/290; VPM: 13%, 9/67; ZI: 33%, 27/82; CP: 49%, 29/59). These results indicate that the effect of postural perturbations in visual thalamus is nonvisual in nature. We then asked how responses to visual stimulation and tilt events interacted. To this end, we analysed the relationship between single unit peristimulus time histograms (PSTHs) recorded under combined visual and tilt stimulations (PSTH VIS+TILT ) and the same unit’s PSTHs recorded under light stimulation alone (PSTH VIS ) and under tilt stimulation in the dark (PSTH TILT ). Specifically, we compared the ability of three different models to fit PSTH VIS+TILT based on PSTH VIS and PSTH TILT : The first model ( eq.1 ) captures a simple gain modulation, in which the amplitude of the visual response is uniformly modulated by the tilt event. The second model ( eq.2 ) consists of a linear combination of light and tilt responses. The third model ( eq.3 ) augments the second with a multiplicative interaction between light and tilt responses. We found that a linear combination of visual and tilt responses provided a substantially better fit compared to the simpler gain modulation model ( Figure 2I, L ; DARK-BRIGHT: p = 0; BRIGHT-DARK: p = 0; rank-sum tests, n = 498) while the addition of a multiplicative interaction did not significantly improve the fit ( Figure 2I, L ; DARK-BRIGHT: p = 0.12; BRIGHT-DARK: p = 0.18; rank-sum tests, n = 498). These results indicate that nonvisual responses to tilts had primarily an additive effect on light responses. Responses to tilt events are robust to changes in expectations It is possible that the observed responses to tilt events reflect a nonspecific “surprise effect” rather than motion itself. To test for this possibility, we modified our original experimental protocol by delivering a loud sound (1046.502 Hz at 102 dB; duration = 0.5s) that reliably signalled the occurrence of a tilt 1.5s later. No sound was delivered in trials in which the platform was kept stationary. To further increase animal’s ability to predict tilt occurrence, the platform was also vibrated throughout the 2s epoch preceding the tilt (see protocol schematic in Supplementary Figure 1E ). We verified, by separate eye tracking experiments (n=4 animals), that these modifications reliably evoked heightened alertness before the tilt events in the form of pupil dilation. Thus, in absence of sound and vibration cues, an increase in pupil size could only be observed ∼0.5s after the tilt ( Supplementary Figure 1D ) while when these cues were present an increase in pupil size occurred ∼1s before the tilt ( Supplementary Figure 1F ). We found that the responses to tilt events in visually responsive cells were preserved in this modified paradigm. Thus, the tilts affected most classes of light responses ( Supplementary Figure 1G, H I, J ); a linear combination of visual and tilt responses provided a better fit compared to alternative models ( Supplementary Figure 1K, L ). These results indicate that the responses to tilt events were maintained even when these events were fully predictable. The responses to tilt events are largely abolished by anaesthesia We next asked whether comparable responses to tilt events occur in anaesthetised animals, in which active motion is abolished. After the induction of a surgical level of anaesthesia (n = 7 animals, 1.5 mg/kg of urethane), animals were placed on a motorised platform designed to deliver tilts along the pitch and roll axes ( Supplementary Figure 2A, B ). An LED, stably mounted on the platform, enabled us to deliver the same visual stimulation when the platform was stationary or tilting. Download figure Open in new tab Supplementary Figure 2. A) Schematic (left) and picture (right) of the motorised platform we used for delivering passive motion to anaesthetised animals. In the schematic we highlight the tilt axes. Animals are placed on the top of the arena and secured by head fixation. B) Gyroscopic measures of the pitch and roll angles during passive motion stimulation. C-K) Same a Figure 2A-I but here we report data collected during passive motion stimulation. The dataset of visual responses in absence of tilts in anaesthetised animals was merged with data from awake animals. This enabled us to classify light responses in anaesthetised conditions along the same five classes described in awake animals ( Supplementary Figure 2C, E , left panel; Supplementary Figure 2D, F , orange lines ). Compared with awake animals, we found that, under anaesthesia, visual responses were only minimally impacted by tilt ( Supplementary Figure 2C, E , mid panel; Supplementary Figure 2D, F , blue lines ). Consistent with this, the amplitude of tilt responses in the dark were negligible when compared with light responses ( Supplementary Figure 2C, E , right panel; Supplementary Figure 2D, F , black lines ). The effect of tilt on light responses was also qualitatively different and, when significant, comprised both increments and decrements in firing rates ( Supplementary Figure 2G, H, I, J ). These smaller effects were best explained by a simple gain modulation model (as in eq.1, see previous section), since more complex models did not significantly improve the fitting ( Supplementary Figure 2K ; p>0.05 across all comparisons, rank-sum tests, n = 303). These results indicate that tilt events evoke qualitatively and quantitatively different responses in anaesthetised animals. Single unit responses express heterogeneous mixed selectivity for active and passive head speed We next asked whether nonvisual responses to tilt events were homogeneous or diverse. To address this question, we applied a clustering analysis to tilt responses recorded in the dark. We included all cells in our anaesthetised and awake datasets that were classified as light responsive. We found 4 main classes of tilt responses ( Figure 3A,C ). The first two classes were observed almost exclusively in awake animals, exhibited different temporal profiles but were both characterised by an overall increase in firing rate ( Figure 3B ). The other two classes were most prominent in anaesthetised animals and characterised by transient increments and decrements in firing rates ( Figure 3B ). In awake animals, expression of the four classes differed across neighbouring thalamic and subthalamic regions. Thus, subthalamic regions overwhelmingly expressed class 2 responses while thalamic units expressed more even proportions of responses across all classes ( Supplementary Figure 3A ; p = 0, Χ 2 = 36.68, n = 430). No significant regional differences were observed in anaesthetised animals (p = 0.62, Χ 2 = 7.15, n = 287). Download figure Open in new tab Supplementary Figure 3. A) Histograms showing the number of units recorded across the four classes determined by our clustering analysis (same colour convention used in Figure 3B, C ). Each histogram represents a separate brain region as identified with histological verification. In each histogram the horizontal line indicates the mean number of units expected in each class under the hypotheses that classes are uniformly expressed. B) Example trials showing five covariates associated with visual stimulation. ON represents light intensity (0 for DARK, 1 for BRIGHT); ON fast and OFF fast capture light onset and offset; ON slow and OFF slow capture slower light adaptation processes known to occur in the visual system. C) Pseudo-R 2 obtained for body speed covariates (x-axis) vs head speed covariates (y-axis) for data obtained during recordings in darkness. Each dot represents an individual unit. D) Pseudo-R 2 obtained for the 12 covariates associated with head speed along the three head axes (x-axis) vs head speed covariates (y-axis). Data obtained during recordings in darkness. E, F) Same as Figure 4D, F but here we used linear instead of angular speed. Download figure Open in new tab Figure 3. A) Normalised PSTHs of single unit responses to tilt in the dark. Units are ordered along the y-axis according to a clustering analysis (see Methods ). The transition between clusters is shown by red lines. B) Histogram showing the number of units counted in each class for the datasets recorded in awake (top panel) and anesthetised (bottom panel) conditions. C) Average PSTH responses across the four classes of tilt responses determined by our cluster analyses. D) Example trials showing normalised readouts of motion signals ( a PM , l PM , a AM , l AM ), position signals ( Sin(Ori), Cos(Ori), DistRot ) and tilt angles ( TiltL, TiltR ). These signals are used as covariates for the GLM analysis. E) Histograms showing goodness-of-fit, measured as pseudo-R 2 (see Methods ), across our dataset of units recorded in the dark. F) The left panel shows the spike counts for an example unit while the middle panel shows its GLM prediction. For ease of visualisation, the trials here are re-ordered by separating the stationary platform condition (bottom trials) from the trials in which we delivered tilt stimulation (top trials). The right panel shows the estimated weight of each covariate for this example unit. G) Weight (Mean ± SEM) of each covariate across our dataset. H) Each dot in the scatterplot shows the weights assigned to l AM and l PM for an individual unit. Units are coloured according to their class as determined by our clustering analysis (same colour convention followed in panels B, C ). I) Increase in pseudo-R 2 for the original set of covariates when compared with a set of covariates in which we shuffled active motion components l AM and a AM (left panel) or passive motion components l PM and a PM (right panel). J-N) Same as panels E-I , but here we analysed our dataset recorded during visual stimulation. To determine the extent to which single units encoded active and passive linear and angular head speed, we estimated the encoding properties of such units by fitting their spike counts in 50ms time bins with Poisson generalised linear models (GLMs, see Methods ). We first applied this analysis to the dataset recorded in the dark. The GLMs employed the set of 4 motion covariates ( l AM , a AM , l PM , a PM ), and this set was augmented with 5 additional covariates describing the head azimuthal orientation within the arena ( Sin(Ori), Cos(Ori) ), the distance from the tilt rotation axis ( DistRot ) and the left and right tilt angles ( TiltL, TiltR ). An illustration of the full set of covariates is provided in Figure 3D . The weights associated with each covariate were estimated by 5-fold cross-validation and the sparseness level in our results was controlled by applying a LASSO regularisation. The goodness-of-fit was then quantified as pseudo-R 2 by predicting held out data (see Methods for details). The activity of most units previously identified as responding to visual stimulation were predicted above chance by these GLMs (80%, n=347/430 units from 9 animals), albeit with variable accuracy ( Figure 3E ). This analysis revealed that individual units typically exhibited mixed selectivity, encoding both active and passive speed components in the weights associated to these covariates (see example cell in Figure 3F ). On average, across our dataset, both active and passive motion components were weighted positively ( Figure 3G ). Nonzero weights were also associated with other non-motion components indicating that animals’ position and orientation within the arena modulated neural responses ( Figure 3G ). The weights associated to active and passive motion components were visibly different across the four classes of tilt responses identified by our clustering analysis ( Figure 3H ). Most notably, class 2 responses assigned larger, more positive weights to passive angular head speed compared with class 1 responses ( Figure 3H , left panel , p = 0, rank-sum test, n = 347). To confirm these results, we set out to determine the extent to which responses from different classes were effectively driven by active and passive motion. To this end we numerically removed the temporal coupling of neural activity with either active ( l AM , a AM ) or passive ( l PM , a PM ) motion components by shuffling these variables. Shuffling of active motion components substantially affected GLM prediction accuracy across all classes of tilt responses ( Figure 3I, left panel; p < 0.0001 for all classes, sign-tests, n = 347). Shuffling of passive motion components also affected all classes, but the reduction in prediction accuracy was most prominent in classes 2 and 4 ( Figure 3I ). Next, we asked whether tilt events were similarly encoded during visual stimulation. We used the same approach described above, but here GLMs were further augmented by five additional covariates capturing sustained and transient features of visual responses (an illustration these additional covariates is provided in Supplementary Figure 3B ). These GLM predicted the activity of most units previously identified as visually responsive (85%, n = 421/498 units from 9 animals) and the accuracy of these predictions was comparable to that obtained during recordings in the dark ( Figure 3J ). Individual units jointly encoded responses to visual stimulation and active and passive motion (see example cell in Figure 3K ). All the main results obtained during recordings in the dark were qualitatively recapitulated under visual stimulation. Thus, the weights assigned to active and passive motion components were overwhelmingly positive ( Figure 3L ); the weights differed across different classes of tilt responses ( Figure 3M ); both active and passive motion components were required to explain single unit responses, albeit their relative contribution differed across response classes ( Figure 3N ). It is also possible that units in our dataset encode the motion of different body parts or that the encoding of head motion is determined by the direction in which the head moves. To test the former possibility, we used signals associated with body instead of head speed. We found that body speed provided less accurate predictions ( Supplementary Figure 3C ; p = 0, sign-test, n = 430), indicating that the head was more strongly represented. To test the latter possibility, we replaced the 4 motion covariates ( l AM , a AM , l PM , a PM ) with the larger set of 12 covariates encompassing angular and linear speed along the three head axes for active and passive motion. This latter analyses also returned less accurate predictions ( Supplementary Figure 3D ; p = 0, sign-test, n = 430). Together, these results indicate that units in dLGN and neighbouring regions encode mixed representations of active and passive head speed. Population responses encode an efficient representation of active and passive head speed Results from clustering and GLM analysis indicate that single units express diverse mixed selectivity for active and passive motion. Here we set out to quantify the representation capacity of these responses at the population level. To answer this question, we analysed a subset of animals (n=5) in which we were able to simultaneously record at least 20 cells that were responsive to light and tilt according to our criteria (see Methods ). We employed two decoding algorithms, a linear decoder based on ridge regression and a nonlinear decoder based on random forest, and we evaluated their performances on held out data (see Methods ). We found that active and passive motion components could be decoded above chance across all animals recorded in the dark (see example active and passive motion signals in Figure 4A, B ) and performances were comparable between linear and nonlinear decoders ( Figure 4C ). We then asked how accurately mixed combinations of active and passive motion could also be decoded from these cell populations. We found that a weighted summation of active and passive angular head speed could be decoded with higher accuracy compared with the decoding of these individual motion components ( Figure 4D , left panel ), and this was true also for linear head speed ( Supplementary Figure 3E , left panel ). Conversely, a weighted difference between active and passive angular head speed was decoded less accurately ( Figure 4D , right panel ) and qualitatively similar results were obtained for linear head speed ( Supplementary Figure 3E , right panel ). Qualitatively matching results were also obtained for the dataset recorded during visual stimulation ( Figure 4F ; Supplementary Figure 3F ). Download figure Open in new tab Figure 4. A) Example trials showing normalised readouts of a AM (blue) and its decoding (red) obtained by training a random forest algorithm on the population response. B) Here we show, for the same example trials, a normalised readout of a PM (blue) and its random forest decoding (red). C) Decoding accuracy (Mean ± SEM), measured as R 2 , for all motion signals motion signals (a PM , l PM , a AM , l AM ) across our dataset obtained by training linear ridge regressions (light grey) and random forests (dark grey). D) The left panel shows the decoding accuracy obtained for weighted summations of a AM and a PM . The grey dots indicate individual animals; the blue dots indicate the average across animals (left panel). The right panel shows the decoding accuracy obtained for weighted subtractions of a AM and a PM . Results shown in panels C and D are obtained during recordings in the dark. E, F) Same as panels C, D but here we show results obtained from recordings during visual stimulation. G) Coefficients of the four principal components obtained from a PCA applied to our dataset of 9 animals recorded in dark and during visual stimulation. H) Decoding accuracy for the projection of motion signals a PM , l PM , a AM , l AM on each principal component for the neural dataset recorded in the dark. I) Same as panel H but here we show results for the neural dataset recorded during visual stimulation. We asked whether this bias towards additive mixed representations could be motivated by coding efficiency. Specifically, we hypothesised that neurons could reduce the number of signals to be transmitted by decorrelating active and passive motion components to minimise redundant information. One way to achieve this, is to perform a principal component analysis (PCA), a linear transformation that can be implemented by biological neurons (see e.g. [ 25 ]). To test for this possibility, we first performed a PCA on our dataset of passive and active angular and linear head speed. We found that the first principal component was represented by a weighted summation of active and passive motion signals, while the second component was represented by the difference between active and passive motion signals ( Figure 4G , see Pc1 & Pc2). Other components, that only captured ∼20% of the overall variance, were represented by differences between angular and linear speed signals ( Figure 4G , see Pc3 & Pc4). We then projected motion signals on the space of the principal components. We found that decoding accuracy for such projections clearly scaled with the variance explained by each component both in dark ( Figure 4H ) and during light stimulation ( Figure 4I ). Together, these results show that subcortical populations of visually responsive neurons primarily encode an efficient, low dimensional representation of head speed. Discussion During natural behaviour, patterns of light entering the eye are largely determined by the subject’s motion. Active motion produced by the subject and passive motion imposed on the subject can occur at the same time and interact with each other (e.g. when passive displacement requires active movements to regain balance [ 9 ]). Thus, key questions to answer are how the visual system jointly represents active and passive motion and the extent to which these motion components are integrated or separated. Our results demonstrate that, during freely moving behaviours, cells in visual thalamus encode a heterogeneous set of mixed representations of active and passive head speed. At the population level, such mixed representations are efficient since they perform dimensionality reduction by exploiting the coupled dynamics of active and passive motion. Firstly, we showed that, in light responsive cells, tilt events comprising active and passive eye, head and body motion evoked non-photic responses, typically consisting of transient increments in firing rate. These responses were widespread and observed across five main types of light responses albeit with different amplitudes. The interaction between responses to tilt events and to light stimulation was well explained by an additive model. To the best of our knowledge, the joint effect of active and passive motion on visual responses has not been previously studied during natural behaviour in freely moving animals. However, the additive nature of such effect, as observed in our data, is consistent with results from cortex V1 in head-fixed animals performing treadmill locomotion [ 4 ] or subjected to passive head movements [ 2 ]. In principle, the responses we observed could be simply driven by surprise rather than motion itself, since trials in which tilt events were delivered were interleaved with static trials according to a pseudorandom sequence. However, we showed that removing this level of uncertainty – by providing a sound cue before the occurrence of a tilt – did not qualitatively affect our results. Instead, suppressing active movements with surgical levels of anaesthesia qualitatively changed the responses to tilt events and substantially reduced their amplitude. The extensive differences in tilt responses between awake and anaesthetised animals are hard to interpret since anaesthesia produces global effects on brain activity that include reduced firing and oscillation frequencies in dLGN [ 26 ] and a global shift in the balance between excitation and inhibition [ 27 ]. Secondly, we show that light responsive cells in dLGN and neighbouring thalamic and subthalamic regions exhibit mixed selectivity for active and passive motion in which both types of motion typically drove an increase in firing rate (see GLM analysis in Figure 3G, L ). Our results are consistent with recent data from V1 and higher order cortical regions [ 3 ]. Furthermore, combining clustering and GLM analyses, we show that individual units exhibit a diverse range of tunings to active and passive motion. Thus, some cells more strongly encoded active motion (classes 1 & 3, Figure 3I ) while others encoded active and passive motion with approximately equal strength (classes 2 & 4, Figure 3I ). This diversity was more prominent in visual thalamus compared with subthalamic regions ( Supplementary Figure 3A ). Together, our data reveal two key properties of how subject’s motion is represented in the visual thalamus. Firstly, combining active and passive motion by mixed selectivity enables to directly estimate the speed of self-motion. This is important information for the visual system since it enables to separate changes in the visual scene due to external factors in the environment (e.g. an approaching object) from changes in the visual scene caused by the motion of the subject. Psychophysics experiments that investigated the visual perception of the speed of the optic flow are consistent with this possibility, showing that perceived speed is reduced by both active and passive subject’s motion [ 28 ]. Secondly, the functional diversity across cells indicates that at least a partial separation of active and passive motion is possible at the level of cell populations. This separation could be performed by regions downstream of the visual thalamus by integrating inputs from thalamic cells differently tuned to active and passive motion signals. How do our results relate to established coding principles in the early visual system? A large body of work has shown that visual response properties are adapted to the statistics of natural scenes in accordance with principles of efficient coding (e.g. [ 16 , 29 - 33 ] but see [ 34 ]). However, visual responses have been primarily recorded in static (anesthetised or head-fixed) subjects. Thus, how subject’s motion is represented and whether this representation is also consistent with efficient coding principles is largely unknown. Here we addressed this question by capturing the statistics of active and passive animal motion during natural behaviour. We showed the speed of self-motion matches the first principal component of active and passive head motion signals while the difference between active and passive head motion signals matches the second principal component ( Figure 4G ). A population decoding analysis showed that the first principal component was more accurately represented compared with individual signals associated with active or passive motion ( Figure 4H, I ). The second principal component was also represented but less accurately. Together, these results indicate that efficient coding principles may also apply to subject’s motion. In this study we primarily targeted dLGN, the main retina relay for cortical vision. Our results indicate that this early stage of the visual pathway encodes a low dimensional representation of subject’s motion and partially separate active and passive motion components. This is consistent with visual properties of cells in this region that have small receptive fields and weaker direction selectivity compared with downstream regions [ 5 , 35 ] and thus are limited in their ability to discriminate different types of visual motion. Cells in visual cortices and higher order thalamic regions are known to better discriminate visual motion thanks to larger receptive fields and stronger direction selectivity [ 5 , 36 ]. In primates, regions along the dorsal visual stream have been shown coordinated and dynamically flexible responses to global optic flow and passive head motion [ 37 , 38 ] and these regions also exhibit differential responses to active and passive head motion [ 39 ]. Thus, an important challenge for future studies will be to determine how the representation of subject’s motion unfolds along the visual pathways during natural freely moving behaviours. Methods Animals Experiments were conducted on 21 adult C57BL/6J mice (19 males, 2 females) from our local colony in Manchester. All mice were initially stored in cages of 5 individuals and housed individually after surgical implantation of the chronic electrode. Animals were provided with food and water ad libitum throughout their life and kept on a 12:12 light dark cycle. Ethical statement Experiments were conducted in accordance with the Animals, Scientific Procedures Act of 1986 (United Kingdom) and approved by the University of Manchester ethical review committee. Surgical Procedures For recovery surgery for brain implants mice were anaesthetised with isoflurane (flow rate: 1.5-2L/min). Concentrations of 4 – 5% and 1 – 1.5% were used respectively for induction and maintenance of anaesthesia. The level of anaesthesia was verified by the lack of withdrawal reflex. After anaesthetic induction the animal head fur was trimmed. The animal was then placed in a stereotaxic frame (Narishige, Japan) and animal’s body temperature was automatically maintained at 37 C by a heating mat while animal’s eyes were protected from drying out by eye drops. Topical application of 1% EMLA cream was followed by a surgical incision to expose the skull. Two slotted cheese machine screws (M1.6x2.0mm, Precision Tools, UK) were inserted respectively into the parietal, and frontal plates to act as anchors for the dental cement and for electrical grounding of the electrode. After craniotomy the electrode was inserted into the dLGN (coordinates from bregma: 2.0-2.2mm medial-lateral, 2.3-2.5 mm rostro-caudal) at a depth of 4-4.5mm from the brain surface. Before brain insertion, electrodes were painted with a fluorescent dye to enable postmortem histological localisation. To assess electrode placement, we monitored light responses during surgical implantation of the electrode. Light-curing cement (X-tra base, VO64434-A, VOCO) was applied to seal the implant. After surgery, the mouse was released from the ear bars and allowed to recover in a single-housed heated cage. Analgesia was provided with a subcutaneous injection of 0.05mg/kg buprenorphine. After the procedure the animal was allowed to recover in a single-housed home-cage for a minimum of six days prior to experimentation. After all data were collected animals were sacrificed and histological post-mortem anatomy was performed to confirm electrode placement. The same recovery procedures (including anaesthesia and analgesia) were used for mice in which we performed eye tracking. In these animals the base of the eye tracker implant was anchored to the skull by using 3 screws, two in left and right parietal plates and one in the frontal plate. Eye tracking cameras were attached to the base before each experimental session by a brief (∼2 minutes) anaesthesia and removed after the end of the session. To record anaesthetised mice on the platform ( Supplementary Figure 2A ) we performed terminal procedures in which the animals were anaesthetised with urethane (1.5mg/kg) and sacrificed on the same day at the end of the experiment. Experimental Set-Up Animals were placed in a small open field arena (dimensions: 20cm x 20cm). The floor of the arena was suspended and attached to the shaft of a digital servo motor (SunFounder, 25Kg, DC 4.8-7.2v) to generate left and right tilts ( Figure 1A, C ). Visual stimulation was supplied by monitors mounted around the arena. The effective irradiance for BRIGHT stimuli was 2.7*1010 photons/cm2/s, 1.4*1013 photons/cm2/s, 1.7*1013 photons/cm2/s and 1.9*1013 photons/cm2/s respectively for S-cone opsins, rhodopsins, melanopsins and M-cone opsins. Video recordings were performed with 8 cameras (Chamaleon 3 from Point Grey; frame rate = 20Hz) mounted over the arena ( Figure 1A ). Infrared cut-on filters (cut-on at 720 nm, Edmund Optics,#65-796) were mounted on each camera to remove visible light. Infrared illumination was provided by two lamps (Edmund Optics; 81mm IR 940nm, #18-607) placed on top of the arena. The direct infrared light projected on the arena was filtered with diffuser films. An illustration of these recordings in provided in Supplementary Movie 1 . Anaesthetised animals were recorded on a custom-made motorised platform controlled by an Arduino Uno board (arduino.cc). The platform rotation was measured using a tri-axial inertial measurement unit (IMU; MPU6050, InvenSense/TDK) mounted to the platform. Before each recording, a brief static calibration was performed to estimate and subtract gyroscope zero-rate offsets, and axis alignment verified using known manual rotations of the platform. Data were sampled at 80Hz. Post hoc, gyroscope readings were converted to physical units (°/s) and any drift observed during stationary periods was corrected for. Extracellular brain recordings were performed with Neuropixel 1.0 electrodes (Imec) and a NI PXIe-1071 acquisition box (National Instruments) running at 30 kHz. Extracellular action potentials were firstly automatically sorted with Kilosort [ 40 ], then manually curated with Phy [ 41 ]. Single unit responses to light and tilt were measured as the distribution of differences between baseline and evoked spike counts across trials. Responses were identified as statistically significant when the p-value of a nonparametric sign-test applied the response distribution was lower than 0.05. The acquisition of neural data was synchronised with the video frame acquisition via TTL pulses driven by an Arduino Uno board (arduino.cc). The same board was also used to control the stepper motor to drive the arena tilts. Psychopy software ([ 42 ], version 2022.2.5) was used to trigger the Arduino Uno board and generate the visual stimulation. Reconstruction of 3D poses We trained Deeplabcut [ 22 ] on ∼2600 manually labelled frames and used to track animals’ and arena 2D keypoint coordinates from individual cameras. These 2D coordinates were triangulated using the direct linear transformation algorithm to estimate animals’ 3D poses and arena 3D coordinates. A statistical shape model (SSM, [ 43 ]) was then estimated on a subset 7000 poses from 7 mice. We used the SSM to fit the 3D poses, correct outliers and fill up missing data as described in [ 44 ]. Separation of Active and Passive Motion The 3D animal’s poses can be expressed as: Where: X ( i ) is an N X x 3 matrix representing respectively the 3D pose of mouse at i th frame (N X is the number of mouse keypoints); X 0 ( i ) represents the animal’s “reference” pose in the centre of the static arena; R ( i ) and T ( i ) are respectively 3 x 3 rotation and N X x 3 translation matrices. We then approximate the effect of active and imposed motion at each frame as a sequential composition of two rigid transformations. According to this approximation, eq.4 can be further decomposed as: Where R A ( i ) and T A ( i ) are rotations and translations matrices associated with active motion, while R I ( i ) and T I ( i ) are associated with passive motion. For simplicity we transformed all 3D arena and mouse coordinates so that R p ( i ) = I 3 (identity matrix) and T p ) = 0 NX X 3 (zero matrix) when the arena is “at rest” before each tilt. The terms R ( i ), T ( i ), R p ( i )and T p ( i )are already given by the 3D reconstruction of the mouse and the arena coordinates. Therefore, we can combine eq.4 and eq.5 to estimate rotation and translation associated with active motion as: Where the superscript T indicates a transpose operation. We then applied R A ( i )and T A ( i )to the animal’s reference pose: The pose X A ( i )represents the animal’s pose after “undoing” the rotation and the translation imposed by the tilt. Therefore, X A ( i )is solely determined by active motion. A comparison between X A ( i )and X ( i )is illustrated in Supplementary Movie 2 . To calculate imposed motion, we first determined the arena’s rotation and translation between two consecutive frames as: We used these transformations to determine the animal’s passive pose at i th frame as: Note that, by using to this definition, we “freeze” mouse pose X ( i − 1) between two consecutive frames. In this way, the only motion accounted for is that imposed by the tilt. To calculate the linear and angular active motion each pair of consecutive poses X A ( i − 1) and X A ( i ) were first realigned to a reference pose centred in the middle of the arena. The alignment transformation was calculated with Procrustes superimposition for the ( i −1) th pose and applied both to the ( i −1) th and the i th pose. We then reapplied Procrustes superimposition to calculate the rotation and translation between the realigned pose pair. Finally, the magnitude of linear active motion and the angular active motion were calculated as: Where: ‖. ‖ indicates the Euclidean norm and trace (·) indicates the trace operator. The angular active motion components associated with egocentric x,y and z axes were extracted from the rotation matrix according to the rotation order Z,Y,X (MATLAB function: rot2eul). To extract linear and angular passive motion we applied the same calculations described for the active case, but we used the poses X ( i − 1) and X p ( i ) instead of X A ( i − 1)and X A ( i ). All motion calculations were then reapplied to the body (excluding head coordinates) in the same way. Eye Tracking Miniaturised camera sensors (OV9734, Omnivision) were used to video animals’ eyes. The sensors were installed in customized tethered acquisition system (Shenzhen Yuweizhixin Electronics Co., Ltd.) equipped with an infrared cut-on filter and infrared LEDs. Frame acquisition for eye tracking was synchronised with frame acquisition from head and body tracking cameras by using Psychopy (version 2022.2.5). An illustration of these experiments is provided in Supplementary Movie 3 . Tracking of the eye keypoints was performed with Deeplabcut [ 22 ]. The measurements of pupil radius and eye movements on the video were first normalised by the distance between inner and the outer canthi, to correct for slight variations in camera angles across the two eyes and across animals. Head and body 3D reconstruction and motion calculations followed the same pipeline described in the previous sections (see Reconstruction of 3D poses and Separation of Active and Passive Motion ). Clustering Analysis Single cell PSTHs were first z-score normalised. The clustering was performed by using a community detection algorithm [ 45 ] as implemented in the brain connectivity toolbox [ 46 ]. This algorithm receives as input an undirected connection matrix and automatically determines the number of cell clusters (or classes). To estimate the connection matrix, we applied K-means across a range of predefined cluster numbers (range: 1-20). We then estimated the connection between cell pairs as the fraction of times in which the pair was assigned to the same cluster by a K-means run. Note that all connection values were bounded between 0 and 1. All clustering analyses were performed on the joint datasets of awake and anaesthetised recordings. GLMs Analysis To fit spike counts from individual cells we used a Poisson GLM regression with canonical link function. We applied lasso regularisation (MATLAB function: lassoglm) to minimise the following loss: Where: β = ( β l ,…, β p )represents the parameters of the model. The regularisation parameter λ was determined for each cell with a five-fold cross-validation. The model parameters were estimated on 50% data while the remaining 50% was used to evaluate goodness of fit. For the latter we first measured residual and null deviances defined as: Where: β saturated represents the parameters of the saturated model in which each observation is fitted exactly and β null the parameters of the model with the intercept only. We used eq.10.1 and eq.10.2 to calculate This measure, equivalent to R 2 in least square estimates, quantifies deviance reduction for maximum likelihood estimates [ 47 ]. To determine the contribution of individual covariates, each covariate was shuffled 5 times and was estimated as average across shuffles. The relative contribution of each covariate ( see Figure 3I, N ) was then calculated as: Population Decoding Analysis We first applied a linear decoder to all simultaneously recorded cells that responded to tilt and light. Estimation of the linear decoder parameters was regularised with ridge regression (MATLAB function: ridge) to minimise the following cost: Where: β = ( β l ,…, β p )represents the parameters of the model, the the vector of spike counts at i th frame, y i the motion speed signal to be decoded. The ridge parameter variable λ was optimised once across all datasets that we used for this analysis. A random forest (MATLAB function: fitensemble) was used to compare the decoding performances of the linear decoder with a nonlinear one. The number of regression trees used by this algorithm was also optimised once across all datasets. A 50% of the data were held out and used to evaluate the decoding performances for both algorithms. Declaration of generative AI and AI-assisted technologies in the manuscript preparation process This study made no use of generative AI and AI-assisted technologies. Author Contributions R.S., A.S.E. and R.S.P designed the study; R.S., M.P.H., A.S.E., Q.H., F.J. performed the experiments; A.S.E., R.S., Z.M., F.P.M., F.J., K.S., R.J. provided source code and analysed the data. R.S., A.S.E. and R.S.P. wrote the manuscript. Declaration of Interests The authors declare no competing interests. Acknowledgements We wish to express thank Robert J Lucas (R.J.L) for intellectual and technical support throughout this study. This study was funded by Sir Henry Dale fellowship from Wellcome Trust to R.S. (220163/Z/20/Z); a research grant by Biotechnology and Biological Sciences Research Council to R.S.P. and R.S. (BB/V009680/1); a Wellcome Trust Investigator award to R.J.L. (210684/Z/18/Z). Funder Information Declared Wellcome Trust, https://ror.org/029chgv08 , 220163/Z/20/Z , 210684/Z/18/Z Biotechnology and Biological Sciences Research Council , BB/V009680/1 Footnotes https://doi.org/10.17605/OSF.IO/DRVFP References 1. ↵ Bouvier , G. , Y. Senzai , and M. 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